To make the mint syrup, put 2 cups water and the sugar in a saucepan over medium heat. Stir until the sugar has dissolved. Add the mint and simmer over low heat for 10 minutes. Remove from the heat and allow to cool, leaving the mint sprigs in the syrup. When completely cool, strain the syrup. Store in a sealable container in the refrigerator. It will keep for two weeks.

Fill a cocktail shaker with ice. Add all the ingredients and shake just to chill. Strain over crushed ice into a glass, such as an old-fashioned. Garnish with a large sprig of mint and add a brown sugar swizzle stick.